k-means Cluster Shape Implications

We present a novel justification why k-means clusters should be (hyper)ball-shaped ones. We show that the clusters must be ball-shaped to attain motion-consistency. If clusters are ball-shaped, one can derive conditions under which two clusters attain the global optimum of k-means. We show further t...

Descripción completa

Detalles Bibliográficos
Autores principales: Kłopotek, Mieczysław A., Wierzchoń, Sławomir T., Kłopotek, Robert A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7256414/
http://dx.doi.org/10.1007/978-3-030-49161-1_10
_version_ 1783539903410208768
author Kłopotek, Mieczysław A.
Wierzchoń, Sławomir T.
Kłopotek, Robert A.
author_facet Kłopotek, Mieczysław A.
Wierzchoń, Sławomir T.
Kłopotek, Robert A.
author_sort Kłopotek, Mieczysław A.
collection PubMed
description We present a novel justification why k-means clusters should be (hyper)ball-shaped ones. We show that the clusters must be ball-shaped to attain motion-consistency. If clusters are ball-shaped, one can derive conditions under which two clusters attain the global optimum of k-means. We show further that if the gap is sufficient for perfect separation, then an incremental k-means is able to discover perfectly separated clusters. This is in conflict with the impression left by an earlier publication by Ackerman and Dasgupta. The proposed motion-transformations can be used to the new labeled data for clustering from existent ones.
format Online
Article
Text
id pubmed-7256414
institution National Center for Biotechnology Information
language English
publishDate 2020
record_format MEDLINE/PubMed
spelling pubmed-72564142020-05-29 k-means Cluster Shape Implications Kłopotek, Mieczysław A. Wierzchoń, Sławomir T. Kłopotek, Robert A. Artificial Intelligence Applications and Innovations Article We present a novel justification why k-means clusters should be (hyper)ball-shaped ones. We show that the clusters must be ball-shaped to attain motion-consistency. If clusters are ball-shaped, one can derive conditions under which two clusters attain the global optimum of k-means. We show further that if the gap is sufficient for perfect separation, then an incremental k-means is able to discover perfectly separated clusters. This is in conflict with the impression left by an earlier publication by Ackerman and Dasgupta. The proposed motion-transformations can be used to the new labeled data for clustering from existent ones. 2020-05-06 /pmc/articles/PMC7256414/ http://dx.doi.org/10.1007/978-3-030-49161-1_10 Text en © IFIP International Federation for Information Processing 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Kłopotek, Mieczysław A.
Wierzchoń, Sławomir T.
Kłopotek, Robert A.
k-means Cluster Shape Implications
title k-means Cluster Shape Implications
title_full k-means Cluster Shape Implications
title_fullStr k-means Cluster Shape Implications
title_full_unstemmed k-means Cluster Shape Implications
title_short k-means Cluster Shape Implications
title_sort k-means cluster shape implications
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7256414/
http://dx.doi.org/10.1007/978-3-030-49161-1_10
work_keys_str_mv AT kłopotekmieczysława kmeansclustershapeimplications
AT wierzchonsławomirt kmeansclustershapeimplications
AT kłopotekroberta kmeansclustershapeimplications

Ejemplares similares